Suffusion is an internal erosion process that is caused by internal instability and involves the “selective erosion of finer particles from the matrix of coarser particles (…) leaving behind a soil skeleton formed by the coarser particles” [6] . For suffusion to occur, the finer fraction of the soil must be less than the available void space in the coarser fraction [22] . A soil that consists predominately of a finer fraction (i.e., a matrix-supported soil) is thus not susceptible to suffusion because the coarser grains are not in grain-to-grain contact but float in the matrix of the finer fraction.

Several opinions on the limit value of the finer fraction for suffusion susceptible soil have been presented in the literature. Wan and Fell [22] argued that the limit is between 22% and 33% and is unlikely to be higher than 40% based on tests on broadly graded samples, while Skempton and Brogan [23] estimated the limit as 35%. Kenney and Lau [15] empirically determined the limit to be 20% based on the lost particles of the unstable widely graded soils that they tested. A widely graded soil is most likely not susceptible to suffusion unless the finer fraction is less than approximately 25% to 35%. According to ICOLD [6] , the finer fraction is determined from the inflection point of the gradation; i.e., the change in slope from the initial slope of the coarse fraction to its transition to the finer fraction (Figure 2(a)). This transition may be difficult to identify. Applications of this procedure to fines-rich and fines-poor glacial till gradations are shown schematically in Figure 2(b).

Although suffusion has been reported to increase the permeability [6] , laboratory studies also indicate that suffusion results in clogging with zones of low permeability, increased gradients and pore pressure build-up [8] [24] . Furthermore, Moffat et al. [10] found that suffusion occurred as the “episodic migration of the finer fraction” with no change in volume but a “relatively small and slow change in local hydraulic conductivity”.

Kezdi [25] and Sherard [7] independently proposed theoretical methods to assess internal stability by splitting the gradation into a fine part and a coarse part (i.e., D₁₅/d₈₅ = 4) to evaluate the self-filtering ability of the soil. However, the split-gradation approaches were not substantiated by laboratory testing. From the outset of the USACE [26] filter experiments, Kenney and Lau [15] [16] studied the internal stability of sand and gravel

specimens in a laboratory setting with permeameter experiments, and Li and Fannin [27] adapted it to include the Kezdi [25] split-gradation method. Burenkova [17] used a different approach to study suffusion susceptibility by dry mixing various fractions and identifying volume changes that occur when finer fractions are introduced. However, Wan and Fell [22] discovered that previous attempts to test the internal stability of soils did not include soils with silt or clay; most of the investigations were on cohesionless sand-gravel mixtures or coarse granular materials, so they conducted seepage tests on clay-silt-sand-gravel and silt-sand-gravel mixtures. Wan and Fell [22] subsequently found that the approach of Burenkova [17] provided satisfactory predictions when analyzing specimens that contain silt.

The approaches by Kenney and Lau [15] [16] and Burenkova [17] , with the respective adaptations by Li and Fannin [27] and Wan and Fell [22] [28] , are discussed further in the following sections.

Based on tests of cohesionless sands and gravels that contain particles up to 100 mm without a silt fraction, Kenney and Lau [15] concluded that soils that experience a loss of fine-grained particles have unstable gradations and conversely that the gradation is stable where there is no loss of particles. Kenney and Lau [15] [16] then proposed a method for evaluating the potential for grading instability; they deduced stable versus unstable gradations based on the shape of the particle size distribution with a limiting-shape curve of H = 1.0F. The method involves determining the mass fraction of particle sizes between D and 4D (denoted by H) and the passing weight at the particle size D (i.e., F); a deficiency in the number of particles of a certain fraction (between D and 4D) will potentially allow for the erosion of particles that are finer than D. For widely graded materials (C_u > 3), the evaluation range is passing weights of 0 to 20%, which is the maximum range for loose particles in such a soil according to Kenney and Lau [15] . Thus, a stability index H/F of less than one indicates that a soil is deficient in the finer fraction and is potentially internally unstable. The evolution of the Kenney and Lau approach is covered in Rönnqvist and Viklander [29] .

Li and Fannin [27] proposed extending the approach of Kenney and Lau [15] [16] to include the criterion of Kezdi [25] . These methods are similar; both examine the slope of the grading curve over a certain length. As reported by Li and Fannin [27] , the Kezdi criterion is incremental over the percentage that is finer by mass, whereas the Kenney-Lau criterion is incremental over the grain size. Figure 3 shows the application of the Kenney-Lau method and Li-Fannin adaptation and how to generate the stability index (H/F)_min from the H:F- shape curve.

Burenkova [17] , who tested cohesionless sand-gravel soils with C_u = d₆₀/d₁₀ values up to 200 and particle sizes up to 100 mm and some silt fractions (less than 10% fines), dry mixed a coarse fraction while gradually introducing a finer fraction. No net change to the volume of the sample indicated that the finer fraction was part of the loose particles and thus susceptible to suffusion. Conversely, an increase in volume would indicate that the finer fraction belongs to the soil skeleton and is therefore structural; thus, it is not susceptible to suffusion. Three soil grain sizes (i.e., d₉₀, d₆₀ and d₁₅) were identified, and a predictive method for assessing the suffusive or non-suffusive characteristics of soils were proposed by combining these sizes into factors of uniformity h' and h" (i.e., d₉₀/d₁₅ and d₉₀/d₆₀, respectively), which define the boundaries for suffusive and non-suffusive soils (Figure 4) [17] .

Based on downward and upward flow seepage tests on clay-silt-sand-gravel and silt-sand-gravel mixtures that are rich in fines, Wan and Fell [22] determined that the Burenkova method gave reasonable correlations to their seepage tests. They adapted the method to include a probabilistic approach that incorporated contours of the probability of internal instability (Figure 4). When the Wan-Fell [22] contours are superimposed over the Burenkova [17] boundaries and zones (Figure 4), the Wan-Fell adaptation is shown to partly cross over into the Burenkova non-suffusive zone.

Wan and Fell [28] subsequently proposed an alternative method for broadly graded soils. They found that gradations that are uniformly graded in the coarse fraction (i.e., steep slope) and broadly graded in the finer fraction (i.e., flat slope) were likely to be internally unstable but were not necessarily predicted to be by the Burenkova method. This alternative method uses the same characteristic D₉₀/D₆₀ value for the coarser fraction but combines it with a value of D₂₀/D₅ for the finer fraction.

In a literature review of laboratory internal stability tests, five studies that involved glacial tills and laboratory suffusion tests were identified [13] . These were the investigations by Lafleur and Nguyen [8] , Wan [9] , Moffat et al. [10] , Hunter et al. [11] , and Lilja et al. [12] , which all incorporated glacial till samples that were either related to, or directly sourced from, dam core zones or transitions.

Compiling these gradations results in an experimental database that includes 11 gradations (Figure 5), whose characteristics are summarized in Table 1; of these, seven gradations are internally unstable according to laboratory tests (i.e., S7, S10, C-20, C-30, CG3, Mr3 and Mr19). Using seepage tests with a gradient of 10, Lafleur and Nguyen [8] found that cohesionless broadly graded glacial tills with fines content up to 12% (with D_max of 38 mm) were susceptible to suffusion, but tills with higher fines content were not susceptible (Table 1). Wan [9] found that when subjected to a constant gradient of 8, a glacial till with 20% fines (with D_max of 4.75 mm) is not susceptible to suffusion. Moffat and Fannin [10] [30] observed suffusive characteristics in a glacial soil with non-plastic fines up to 30% (with D_max of 20 mm). Furthermore, based on seepage tests, Lilja et al. [12] reported internal instability in glacial tills with fines between 25% to 35% (with D_max of 30 mm). While investigating global backward erosion, Hunter et al. [11] found that the coarse test grading CG3 experienced backward erosion but concluded that suffusion most likely indirectly influenced the process.

The studied gradations comprise glacial till soils with the fines content (passing 0.075 mm when regraded on the

^aMass passing 0.075 mm of the full sample; brackets indicate that it is regraded to #4 sieve (i.e., 4.75 mm); ^bPoint of inflection on the gradation curve.

4.75 mm sieve) of 8% to 43% and coefficients of uniformity (C_u = d₆₀/d₁₀) of 6 to 425 (Table 1). Several of the gradations have finer fractions that exceed 35% (i.e., gradations S28, S17, RD, FG1, and Mr19) and are thus potentially not susceptible to suffusion. This will be addressed in the analyses in the following sections.

In a study of the possibility of extending the Kenney-Lau method [15] [16] to gradations that include a fraction of non-cohesive silt, specifically glacial till, the gradations of the core soil of glacial till belonging to 74 existing dams were analyzed [14] . Performance monitoring data described in published and unpublished reports were used to identify 23 of the dams in which internal erosion has been documented; the other 51 dams have no records of deficiencies that can be reasonably attributed to internal erosion. Thus, the dams were sorted into 1) dams with the probable occurrence of internal erosion, and 2) dams with no observations that indicate internal erosion.

The Kenney-Lau method [15] [16] evaluates the potential for internal stability by analyzing the shape of the finer end of the gradation curve. The Li-Fannin adaptation [27] incorporates the Kezdi [25] split-gradation method. The H:F-shape curves of the most vulnerable core gradations are shown in Figure 7, and the corresponding stability indexes (i.e., H/F_min) are shown in Figure 8(a). The stability index is the smallest value along the H:F curve within the evaluation range is mass passing 0 to 20% (for widely graded materials, C_u = d₆₀/d₁₀ > 3), as indicated in Figure 7 and Figure 8).

A summary of the analyses (Table 4) shows that the Kenney-Lau method identifies 75% of the unstable gradations and that 56% of the potentially unstable gradations are gradations that tested or performed as unstable (Figure 8(a)). Disregarding the gradations with finer fraction > 35% (not susceptible to suffusion), 82% of the unstable gradations were identified. The equivalent values for the Li-Fannin adaptation are 67% and 67%, respectively (Figure 8(b), Table 4).

The Burenkova method [17] evaluates the potential for internal instability using a characteristic value for the slope of the coarser fraction (D₉₀/D₆₀) and the overall slope of the gradation curve (D₉₀/D₁₅). The Wan-Fell adaptation [22] incorporates a probabilistic approach within the same framework of the grain size ratio. The distribution of gradations from the Burenkova method is given in Figure 9, and the distribution from the Wan-Fell adaptation is shown in Figure 10.

A summary of the analyses (Table 4) of the most vulnerable core gradations shows that the Burenkova method identifies 58% of the unstable gradations and that 47% of the potentially unstable gradations are gradations which have tested or performed as unstable (Figure 9). The equivalent values for the Wan-Fell adaptation are 8% and 50%, respectively (Figure 10, Table 4) for a greater than 5% probability of internal instability (for silt-sand-gravel soils and clay-silt-sand-gravel soils with limited clay contents and plasticity).

^aResults when gradations with finer fraction > 35% are excluded (i.e., S17, S28, RD, FG1, Mr19 and 22); ^bGradations RD, FG1, CG3, S, N, 11, 26 and 54 are not included because gradation data on minus #200 sieve are not available.

Recognizing that the Burenkova approach may not provide accurate predictions for gradations that are uniform in the coarse fraction and broad in the finer fraction, Wan and Fell [28] proposed that the potential for internal instability in these broadly graded soils be evaluated using the same characteristic D₉₀/D₆₀ value for the coarser fraction but with a value of D₂₀/D₅ for the finer fraction. The distribution of gradations is shown in Figure 11.

A summary of the analyses (Table 4) for the most vulnerable core gradation shows that the Wan-Fell alternative method predicts that none of the gradations are potentially unstable (located in the unstable or transition region).